A fuzzy system based active set algorithm for the numerical solution of the optimal control problem governed by partial differential equation

A computational indirect method based on a fuzzy system technique and active set strategy is presented. This new method has been used for the numerical solution of an optimal control problem governed by elliptic partial differential equation. To solve this problem, we start with obtaining the first-order necessary optimality conditions, which contain a mixed variational inequality in function space. Then a fuzzy basis functions technique combined with a primal-dual active set method to derive a new efficient algorithm for solving the given problem. Finally, some numerical examples are given to illustrate the accuracy and efficiency of the proposed technique.